Sample Space
A Set of all possible outcomes of an experiment
In probability theory, the sample space is the set of all possible outcomes or events that can occur in a given experiment or situation. It is denoted by the letter S and can be represented in various ways, such as by a list, a table, or a diagram.
For example, if we toss a coin, the sample space consists of two outcomes: heads and tails. Therefore, S = {H, T}. Similarly, if we roll a six-sided die, the sample space consists of six outcomes: 1, 2, 3, 4, 5, and 6. Therefore, S = {1, 2, 3, 4, 5, 6}.
In some cases, the sample space can be very large or infinite. For instance, if we flip a coin three times, the sample space would consist of eight outcomes: HHH, HHT, HTH, HTT, THH, THT, TTH, and TTT. Therefore, S = {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}.
Understanding the sample space is fundamental in constructing probability models and making accurate predictions about the likelihood of certain outcomes. It is also useful in solving problems related to permutations, combinations, and other mathematical concepts.
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